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arXiv:physics/0206048 · Physical Review A

Spontaneous emission rate of an excited atom placed near a nanofiber

В. В. Климов, M. Ducloy

Published Jan 22, 2004• 158 citations
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Abstract

The spontaneous decay rate of an excited atom placed near a dielectric cylinder is investigated. Special attention is paid to the case when the cylinder radius is small in comparison with radiation wavelength (nanofiber or photonic wire). In this case, the analytical expressions of the transition rates for different orientations of a dipole are derived. It is shown that the main contribution to decay rates is due to the quasistatic interaction of the atom dipole momentum with the nanofiber, and the contributions of guided modes are exponentially small. On the contrary, in the case when the radius of the fiber is only slightly less than the radiation wavelength, the influence of guided modes can be substantial. The results obtained are compared with the case of a dielectric nanospheroid and an ideally conducting wire.

DOI
10.1103/physreva.69.013812

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The spontaneous decay rate of an excited atom placed near a dielectric cylinder is investigated. Special attention is paid to the case when the cylinder radius is small in comparison with radiation wavelength (nanofiber or photonic wire). In this case, the analytical expressions of the transition rates for different orientations of a dipole are derived. It is shown that the main contribution to decay rates is due to the quasistatic interaction of the atom dipole momentum with the nanofiber, and the contributions of guided modes are exponentially small. On the contrary, in the case when the radius of the fiber is only slightly less than the radiation wavelength, the influence of guided modes can be substantial. The results obtained are compared with the case of a dielectric nanospheroid and an ideally conducting wire.
The effect of nanobodies, i.e., the bodies whose size is small compared to the emission wavelength, on spontaneous emission of an atom located near them is considered. The results of calculations performed within the framework of quantum and classical electrodynamics are presented both in analytic and graphical forms and can be readily used for planning experiments and analysis of experimental data. It is shown that nanobodies can be used to control efficiently the rate of spontaneous transitions. Thus, an excited atom located near a nanocylinder or a nanospheroid pole, whose transition dipole moment is directed normally to the nanobody surface, can decay with the rate that is tens and hundreds times higher than the decay rate in a free space. In the case of some (negative) dielectric constants, the decay rate can increase by a factor of 10 5 —10 6 and more. On the other hand, the decay of an excited atom whose transition dipole moment is directed tangentially to the nanobody surface substantially slows down. The probability of nonradiative decay of the excited state is shown to increase substantially in the presence of na-nobodies possessing losses.
We study the spontaneous emission of a cesium atom in the vicinity of a subwavelength-diameter fiber. We show that the confinement of the guided modes and the degeneracy of the excited and ground states substantially affect the spontaneous emission process. We demonstrate that different magnetic sublevels have different decay rates. When the fiber radius is about 200nm200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}200nm, a significant fraction (up to 28%) of spontaneous emission by the atom can be channeled into guided modes. Our results may find applications for developing nanoprobes for atoms and efficient couplers for subwavelength-diameter fibers.
We investigate the radiative coupling between two two-level atoms with arbitrarily polarized dipoles in the vicinity of a nanofiber. We present a systematic derivation for the master equation, the single- and cross-atom decay coefficients, and the dipole-dipole interaction coefficients for the atoms interacting with the vacuum of the field in the guided and radiation modes of the nanofiber. We study numerically the case where the atomic dipoles are circularly polarized. In this case, the rate of emission depends on the propagation direction along the fiber axis and, hence, the radiative interaction between the atoms is chiral. We examine the time evolution of the atoms for different initial states. We calculate the fluxes and mean numbers of photons spontaneously emitted into guided modes in the positive and negative directions of the fiber axis. We show that the chiral radiative coupling modifies the collective emission of the atoms. We observe that the modifications strongly depend on the initial state of the atomic system, the radiative transfer direction, the distance between the atoms, and the distance from the atoms to the fiber surface.
Nanofibers are a valuable tool for interfacing photons with atomic media through its guided mode which propagates evanescent to the fiber. However, the nanofiber modifies the natural decay rate of the atomic dipoles due to the Purcell effect. It is vital to study these atom-fiber interactions to characterize the system. This thesis delineates an experimental technique to obtain the spontaneous emission rate of a cloud of Rubidium-87 atoms in the presence of a nanofiber. The atoms are prepared in a magneto optical trap and the emissions are monitored by balanced homodyne detection. The temporal autocorrelation function of the homodyne’s photocurrent reproduces the exponential profile of spontaneous emission. The measured time constant of the profile is 26.3 ns which is almost twice that of free space emission. The modified decay rate depends on the atom’s orientation and distance from the nanofiber surface. We theoretically estimate the modified decay rate and model the expected decay profile for our ensemble of atoms which agrees well with our measurements. To our knowledge, this is the first experimental demonstration of spontaneous emission being measured by homodyne detection.
We investigate the radiative coupling between two two-level atoms with arbitrarily polarized dipoles in the vicinity of a nanofiber. We present a systematic derivation for the master equation, the single- and cross-atom decay coefficients, and the dipole-dipole interaction coefficients for the atoms interacting with the vacuum of the field in the guided and radiation modes of the nanofiber. We study numerically the case where the atomic dipoles are circularly polarized. In this case, the rate of emission depends on the propagation direction, that is, the radiative interaction between the atoms is chiral. We examine the time evolution of the atoms for different initial states. We calculate the fluxes and mean numbers of photons spontaneously emitted into guided modes in the positive and negative directions of the fiber axis. We show that the chiral radiative coupling modifies the collective emission of the atoms. We observe that the modifications strongly depend on the initial state of the atomic system, the radiative transfer direction, the distance between the atoms, and the distance from the atoms to the fiber surface.
We present calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.